from manim import *
class CustomCurve(VMobject):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        # 定义自定义曲线的控制点
        points = [
            [8, 3, 0],
            [6,-3,0],
            [3,-5,0],
            [6,-7,0],
            [8,-13,0],
        ]
        self.set_points_smoothly(points)
class CustomCurve1(VMobject):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        # 定义自定义曲线的控制点
        points = [
            [18, 4, 0],
            [22,-12,0],
            [43,-16,0]
        ]
        self.set_points_smoothly(points)

class math1(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(6*2+1):       
            dot1=Dot([-50,5*(i-6),0]).set_opacity(0.5)
            dot2=Dot([50,5*(i-6),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(10*2+1):        
            dot3=Dot([(i-10)*5,-30,0]).set_opacity(0.5)
            dot4=Dot([(i-10)*5,30,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #镜头跟进效果 
        self.camera.frame.save_state()
         #题目出现
        text = Tex(r"\text{(张1000题5)设p为常数,若反常积分$\int _{0}^{1}\dfrac{\ln x}{x^{p}\left( 1-x\right) ^{1-p}}dx$\text{收敛,则p的范围:}}"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,20,0])
        text1 = Tex(
                   r"\text{(A)}$\left( -1,1\right) $"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-22,15,0])
        text2 = Tex(
                    r"\text{(B)}$\left( -1,2\right) $"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([22,15,0])
        text3 = Tex(
                   r"\text{(C)}$\left( -\infty ,1\right) $"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-22,8,0])
        text4 = Tex(
                    r"\text{(D)}$\left( -\infty ,2\right) $"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([22,8,0])

        self.play(Write(text),Write(text1),Write(text2),Write(text3),Write(text4))
        self.wait(0.1)
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(Restore(self.camera.frame))
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #题目向上移动
        #self.play(text.animate().move_to([0,20,0]),text1.animate().move_to([-22,15,0]) ,text2.animate().move_to([22,15,0]),text3.animate().move_to([-22,8,0]),text4.animate().move_to([22,8,0]) )

        text1 = Tex(
                    r"\text{瑕点为}$0$\text{和}$1$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-36,0,0])
        self.play(Write(text1))
        text2 = Tex(
                    r"\text{当}$x\rightarrow 0 $",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-45,-5,0])
        self.play(Write(text2))
        text3 = Tex(
                    r"$\int _{0}^{1}\dfrac{\ln x}{x^{p}\left( 1-x\right) ^{1-p}}dx$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-28,-5,0])
        self.play(Write(text3))
        text4 = Tex(
                    r"\text{等价于}$\int _{0}^{1}\dfrac{\ln x}{x^{p}}dx$",color=PURPLE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-7,-5,0])
        self.play(Write(text4))
        
        #画曲线
        curve = CustomCurve(color=RED, stroke_width=20)
        
        # 添加到场景并播放动画
        self.play(Create(curve))
        self.wait(0.5)





        text5 = Tex(
                    r"$p>1$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([13, 3, 0])
        
        text6 = Tex(
                    r"$p=1$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([13,-5,0])
        text7 = Tex(
                    r"$p<1$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([13,-13,0])
        
        text8 = Tex(
                    r"$x\gg \ln x$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([-20,-15,0])



        self.play(Write(text5),Write(text6),Write(text7))

        self.play(Write(text8))

        text9 = Tex(
                    r"\text{与}$\dfrac{1}{x^{p}}$\text{同趋势}",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([27, 3, 0])
        self.play(Write(text9))
        text11 = Tex(
                    r"\text{(发散)}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([40,3,0])
        self.play(Write(text11))

        text12 = Tex(
                    r"\text{与}$\dfrac{1}{x^{p}}$\text{同趋势}",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([27, -13, 0])
        self.play(Write(text12),FadeOut(text8))
        text13 = Tex(
                    r"\text{(收敛)}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([40,-13,0])
        self.play(Write(text13))
        
        text14 = Tex(
                    r"$\int ^{1}_{0}\dfrac{\ln x}{x}dx$",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        self.play(Write(text14))
        text15 = Tex(
                    r"$\int ^{1}_{0}\ln xd\ln x$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        text16 = Tex(
                    r"$\int _{-\infty }^{0}tdt$",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-15,0])
        self.play(
            ReplacementTransform(text14,text15)
        )
        self.wait(0.5)
        self.play(
            
            ReplacementTransform(text15,text16)
        )
        text17 = Tex(
                    r"$\text{(发散)}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10,-15,0])
        self.play(Write(text17))
        self.wait(0.5)
        text18 = Tex(
                    r"$\text{(发散)}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([30,-5,0])
        self.play(Write(text18))
        text19 = Tex(
                    r"$p<1$",color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,12,0])
        self.play(Write(text19))
        self.wait(0.5)
        self.play(Uncreate(text18),Uncreate(text17),Uncreate(text16),Uncreate(text13)
                  ,Uncreate(text12),Uncreate(text11),Uncreate(text9)
                  ,Uncreate(text8),Uncreate(text7),Uncreate(text6)
                  ,Uncreate(text5),Uncreate(text4),Uncreate(text3)
                  ,Uncreate(text2),Uncreate(curve))
        




        text2 = Tex(
                    r"\text{当}$x\rightarrow 1$",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-40,-5,0])
        self.play(Write(text2))
        text3 = Tex(
                    r"$\dfrac{\ln x}{x^{p}\left( 1-x\right) ^{1-p}}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-28,-5,0])
        self.play(Write(text3))
        text4 = Tex(
                    r"\text{等价于}$\dfrac{x-1}{\left( 1-x\right) ^{1-p}}$",color=WHITE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-7,-5,0])
        self.play(Write(text4))
        text40 = Tex(
                    r"\text{等价于}$\dfrac{1}{\left( 1-x\right) ^{-p}}$",color=PURPLE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-7,-5,0])
        self.play(
            ReplacementTransform(text4,text40)
        )
        self.wait(0.5)
        
        text9 = Tex(
                    r"\text{令}$1-x=t$",color=BLUE
                   ,tex_template=TexTemplateLibrary.ctex).scale(8.0).move_to([17, -5, 0])
        self.play(Write(text9))

        text2 = Tex(
                    r"\text{当}$t\rightarrow 0$",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-40,-15,0])
        self.play(Write(text2))
        text3 = Tex(
                    r"$\dfrac{1}{t^{-p}}$",color=PURPLE
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-28,-15,0])
        self.play(Write(text3))
        text3 = Tex(
                    r"\text{-p<1时(收敛)}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-15,0])
        self.play(Write(text3))
        
        text19 = Tex(
                    r"$p>-1$",color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,8,0])
        self.play(Write(text19))
        self.wait(0.5)
        #半透明矩阵扩展
        rectangle4=Rectangle(color=GREEN,fill_opacity=0.5,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-22,15,0])
        self.play(
            rectangle4.animate.stretch(16.0,dim=0)
        )
        








        self.wait()